OF ARTS AND SCIENCES: OCTOBER 13, 1863. 169 



Professor Peirce presented an account of a ternary system 

 of arithmetical notation, consisting of the three characters 1, 0, 

 and 1 (minus one being written in the manner of the negative 

 characteristics of logarithms). This system has the same 

 property as the binary system discussed by Leibnitz, namely, 

 that of reducing the processes of multiplication and division to 

 series of additions and subtractions. It would require to ex- 

 press the same values about twice as many figures as the deci- 

 mal system ; but, as these are the simple characters 1, 0, 1, they 

 would occupy but little more room on the printed page. 



Professor Peirce considered the probable consequences of an 

 adoption of such a system for the uses of life, and thought that, 

 if this notation could ever have come into use, it would have 

 been converted into a system of nine figures by the union in 

 pairs of the fundamental characters. 



Five hundred and t'wenty-sixtli Meeting. 



October 13, 1863. — Monthly Meeting. 



The President in the chair. 



Professor Bond presented a communication " On the new 

 form of the Achromatic Object-Glass recently introduced by 

 Steinheil." 



In June, 1860, Professor Steinheil communicated to the Royal 

 Academy of Sciences at Munich * a notice of an object-glass of thirty- 

 six lines aperture, executed at his optical establishment according to 

 the system of curves proposed by Gauss in an article published in the 

 Zeitschrift fur Astronomie of Lindenau and Bohnenberger, in 1817.t 



This telescope, and subsequently another % of similar form, but 

 larger, have been carefully tested, and, in the opinion of competent 



* Sitzungsberichte der konigl. bayer. Akademie der Wissenschaften zu Miin- 

 chen, 1860, II. 160. 



t Lindenau und Bohnenberger, Zeitschrift fiir Astronomie, Nov., Dec. 1817, 

 IV. 345. 



X Sitzungsberichte, 1860, V. 662. 

 VOL. VI. 17 



